The right-arm medium pacer dismissed Aaron Finch (49) and the Marsh brothers — Shaun and Mitchell – for ducks as Australia slumped from 87 without loss to finish the fourth day at 136-3.
At stumps opener Usman Khawaja was batting on a fighting 50 and Travis Head on 34 as the pair had added an invaluable 49 for the unbroken fourth wicket stand to prolong Australia’s resistance on a weary and spinning Dubai stadium pitch.
Pakistan will need seven more wickets while Australia require another 326 runs for an improbable victory to take a 1-0 lead in the two-match series.
The second Test starts in Abu Dhabi from 16 October.
It was an action replay of the first innings as Australian openers put on 87 — they made 142 in their total of 202 on Tuesday — as Finch was trapped leg-before soon after tea with a sharp incoming delivery from Abbas.
Finch, who took an unsuccessful review, hit five boundaries in his knock.
Two balls later Abbas had the elder Marsh caught behind and in his next over trapped Mitchell right in front of the stumps only to get the decision on review.
But it was Finch and Khawaja in the afternoon session who batted with resolve.
Pakistan-born Khawaja, who top scored for Australia with 85 in the first innings, held one end intact with resolute batting, having so far hit six boundaries.
Abbas has figures of 3-26 to add to his four wickets in the first innings, but leg-spinner Yasir Shah was still wicketless in the match.
If Australia still wish to win this match they will have to rewrite the history books as the highest chase in all Test cricket is West Indies’s 418-7, made against Australia at Antigua in 2003.
Pakistan, who were 45 for three overnight, declared 7.5 overs after lunch on 181-6 at the fall of Asad Shafiq’s wicket for 41.
Pakistan made 482 in their first innings while in reply Australia were dismissed for 202.
Jon Holland, who took the key wicket of Azhar Ali for four on Tuesday, dismissed opener Imam-ul-Haq for 48, caught and bowled off a flighted delivery.
Debutant Marnus Labuschagne then had Haris Sohail caught close to the slips for 39, leaving Pakistan at 110-4. Sohail and Imam had added 65 runs for the fourth wicket.
Holland had figures of 3-83 from 20 overs while off-spinner Nathan Lyon took 2-58.